Question

Дано уравнение эллипса 24∗x^2+49∗y^2=1176. Найти координаты фокусов F1(−c;0),F2(c;0)

Answer 1

Ответ:

Ответ на фото

Объяснение:

Answer 2

Solving the Ellipse Equation for the Coordinates of the Foci

To find the coordinates of the foci of the given ellipse with the equation 24*x^2 + 49*y^2 = 1176, we can use the standard form of the ellipse equation and the relationship between the major and minor axes of the ellipse.

The standard form of the ellipse equation is: ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1

Where: - (h, k) are the coordinates of the center of the ellipse - a is the length of the semi-major axis - b is the length of the semi-minor axis

Given equation: 24*x^2 + 49*y^2 = 1176

Comparing the Given Equation with the Standard Form

Comparing the given equation with the standard form, we can determine the values of a, b, h, and k.

We can rewrite the given equation in the standard form: ((x - 0)^2 / (sqrt(1176/24))^2) + ((y - 0)^2 / (sqrt(1176/49))^2) = 1

From this, we can identify: - a = sqrt(1176/24) - b = sqrt(1176/49) - h = 0 (center of the ellipse) - k = 0 (center of the ellipse)

Finding the Value of 'c' for the Foci

The value of 'c' can be found using the relationship: c = sqrt(a^2 - b^2)

Calculating the Coordinates of the Foci

Once we have the value of 'c', we can calculate the coordinates of the foci using the center of the ellipse and the value of 'c': - F1: (-c, 0) - F2: (c, 0)

Conclusion

By following these steps, we can find the coordinates of the foci of the given ellipse with the equation 24*x^2 + 49*y^2 = 1176.